# Copyright 2022 UC Berkeley Team and The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, deprecate
from .scheduling_utils import SchedulerMixin


@dataclass
class DDPMSchedulerOutput(BaseOutput):
    """
    Output class for the scheduler's step function output.

    Args:
        prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
            denoising loop.
        pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
            `pred_original_sample` can be used to preview progress or for guidance.
    """

    prev_sample: torch.FloatTensor
    pred_original_sample: Optional[torch.FloatTensor] = None


def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
    """
    Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
    (1-beta) over time from t = [0,1].

    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
    to that part of the diffusion process.


    Args:
        num_diffusion_timesteps (`int`): the number of betas to produce.
        max_beta (`float`): the maximum beta to use; use values lower than 1 to
                     prevent singularities.

    Returns:
        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
    """

    def alpha_bar(time_step):
        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
    return torch.tensor(betas, dtype=torch.float32)


class DDPMScheduler(SchedulerMixin, ConfigMixin):
    """
    Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
    Langevin dynamics sampling.

    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
    [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
    [`~ConfigMixin.from_config`] functions.

    For more details, see the original paper: https://arxiv.org/abs/2006.11239

    Args:
        num_train_timesteps (`int`): number of diffusion steps used to train the model.
        beta_start (`float`): the starting `beta` value of inference.
        beta_end (`float`): the final `beta` value.
        beta_schedule (`str`):
            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
        trained_betas (`np.ndarray`, optional):
            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
        variance_type (`str`):
            options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`,
            `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
        clip_sample (`bool`, default `True`):
            option to clip predicted sample between -1 and 1 for numerical stability.

    """

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[np.ndarray] = None,
        variance_type: str = "fixed_small",
        clip_sample: bool = True,
        **kwargs,
    ):
        deprecate(
            "tensor_format",
            "0.6.0",
            "If you're running your code in PyTorch, you can safely remove this argument.",
            take_from=kwargs,
        )

        if trained_betas is not None:
            self.betas = torch.from_numpy(trained_betas)
        elif beta_schedule == "linear":
            self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            self.betas = (
                torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
            )
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        elif beta_schedule == "sigmoid":
            # GeoDiff sigmoid schedule
            betas = torch.linspace(-6, 6, num_train_timesteps)
            self.betas = torch.sigmoid(betas) * (beta_end - beta_start) + beta_start
        else:
            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
        self.one = torch.tensor(1.0)

        # standard deviation of the initial noise distribution
        self.init_noise_sigma = 1.0

        # setable values
        self.num_inference_steps = None
        self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy())

        self.variance_type = variance_type

    def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.

        Args:
            sample (`torch.FloatTensor`): input sample
            timestep (`int`, optional): current timestep

        Returns:
            `torch.FloatTensor`: scaled input sample
        """
        return sample

    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.

        Args:
            num_inference_steps (`int`):
                the number of diffusion steps used when generating samples with a pre-trained model.
        """
        num_inference_steps = min(self.config.num_train_timesteps, num_inference_steps)
        self.num_inference_steps = num_inference_steps
        timesteps = np.arange(
            0, self.config.num_train_timesteps, self.config.num_train_timesteps // self.num_inference_steps
        )[::-1].copy()
        self.timesteps = torch.from_numpy(timesteps).to(device)

    ## Modified DDPM get variance
    # def _get_variance(self, t, predicted_variance=None, variance_type=None):
    #     alpha_prod_t = self.alphas_cumprod[t]
    #     alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one

    #     # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
    #     # and sample from it to get previous sample
    #     # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
    #     variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]

    #     if variance_type is None:
    #         variance_type = self.config.variance_type

    #     # hacks - were probably added for training stability
    #     if variance_type == "fixed_small":
    #         variance = torch.clamp(variance, min=1e-20)
    #     # for rl-diffuser https://arxiv.org/abs/2205.09991
    #     elif variance_type == "fixed_small_log":
    #         variance = torch.log(torch.clamp(variance, min=1e-20))
    #     elif variance_type == "fixed_large":
    #         variance = self.betas[t]
    #     elif variance_type == "fixed_large_log":
    #         # Glide max_log
    #         variance = torch.log(self.betas[t])
    #     elif variance_type == "learned":
    #         return predicted_variance
    #     elif variance_type == "learned_range":
    #         min_log = variance
    #         max_log = self.betas[t]
    #         frac = (predicted_variance + 1) / 2
    #         variance = frac * max_log + (1 - frac) * min_log

    #     return variance

    ## Modified DDPM step
    # def step(
    #     self,
    #     model_output: torch.FloatTensor,
    #     timestep: int,
    #     sample: torch.FloatTensor,
    #     predict_epsilon=True,
    #     generator=None,
    #     return_dict: bool = True,
    # ) -> Union[DDPMSchedulerOutput, Tuple]:
    #     """
    #     Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
    #     process from the learned model outputs (most often the predicted noise).

    #     Args:
    #         model_output (`torch.FloatTensor`): direct output from learned diffusion model.
    #         timestep (`int`): current discrete timestep in the diffusion chain.
    #         sample (`torch.FloatTensor`):
    #             current instance of sample being created by diffusion process.
    #         predict_epsilon (`bool`):
    #             optional flag to use when model predicts the samples directly instead of the noise, epsilon.
    #         generator: random number generator.
    #         return_dict (`bool`): option for returning tuple rather than DDPMSchedulerOutput class

    #     Returns:
    #         [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] or `tuple`:
    #         [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
    #         returning a tuple, the first element is the sample tensor.

    #     """
    #     t = timestep

    #     if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
    #         model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1)
    #     else:
    #         predicted_variance = None

    #     # 1. compute alphas, betas
    #     alpha_prod_t = self.alphas_cumprod[t]
    #     alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one
    #     beta_prod_t = 1 - alpha_prod_t
    #     beta_prod_t_prev = 1 - alpha_prod_t_prev

    #     # 2. compute predicted original sample from predicted noise also called
    #     # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
    #     if predict_epsilon:
    #         pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
    #     else:
    #         pred_original_sample = model_output

    #     # 3. Clip "predicted x_0"
    #     if self.config.clip_sample:
    #         pred_original_sample = torch.clamp(pred_original_sample, -1, 1)

    #     # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
    #     # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
    #     pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * self.betas[t]) / beta_prod_t
    #     current_sample_coeff = self.alphas[t] ** (0.5) * beta_prod_t_prev / beta_prod_t

    #     # 5. Compute predicted previous sample µ_t
    #     # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
    #     pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

    #     # 6. Add noise
    #     variance = 0
    #     if t > 0:
    #         noise = torch.randn(
    #             model_output.size(), dtype=model_output.dtype, layout=model_output.layout, generator=generator
    #         ).to(model_output.device)
    #         variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * noise

    #     pred_prev_sample = pred_prev_sample + variance

    #     if not return_dict:
    #         return (pred_prev_sample,)

    #     return DDPMSchedulerOutput(prev_sample=pred_prev_sample, pred_original_sample=pred_original_sample)
    
    # def _get_variance(self, t, predicted_variance=None, variance_type=None):
    #     ### Missing
    #     prev_t = self.previous_timestep(t)

    #     alpha_prod_t = self.alphas_cumprod[t]
    #     ### alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one
    #     alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one
    #     current_beta_t = 1 - alpha_prod_t / alpha_prod_t_prev ### Added

    #     # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
    #     # and sample from it to get previous sample
    #     # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
        
    #     ### variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
    #     variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * current_beta_t

    #     if variance_type is None:
    #         variance_type = self.config.variance_type

    #     # hacks - were probably added for training stability
    #     if variance_type == "fixed_small":
    #         variance = torch.clamp(variance, min=1e-20)
    #     # for rl-diffuser https://arxiv.org/abs/2205.09991
    #     elif variance_type == "fixed_small_log":
    #         variance = torch.log(torch.clamp(variance, min=1e-20))
    #     elif variance_type == "fixed_large":
    #         variance = self.betas[t]
    #     elif variance_type == "fixed_large_log":
    #         # Glide max_log
    #         variance = torch.log(self.betas[t])
    #     elif variance_type == "learned":
    #         return predicted_variance
    #     elif variance_type == "learned_range":
    #         min_log = variance
    #         max_log = self.betas[t]
    #         frac = (predicted_variance + 1) / 2
    #         variance = frac * max_log + (1 - frac) * min_log

    #     return variance
    
    ### DDIM get_variance
    def _get_variance(self, timestep, prev_timestep):
        alpha_prod_t = self.alphas_cumprod[timestep]
        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else torch.tensor(1.0)
        beta_prod_t = 1 - alpha_prod_t
        beta_prod_t_prev = 1 - alpha_prod_t_prev

        variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
        
        return variance
    
    ### Modified DDIM step
    # def step(
    #     self,
    #     model_output: torch.FloatTensor,
    #     timestep: int,
    #     sample: torch.FloatTensor,
    #     eta: float = 0.0,
    #     use_clipped_model_output: bool = False,
    #     generator=None,
    #     variance_noise: Optional[torch.FloatTensor] = None,
    #     return_dict: bool = True,
    # ) -> Union[DDPMSchedulerOutput, Tuple]:
    #     """
    #     Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
    #     process from the learned model outputs (most often the predicted noise).

    #     Args:
    #         model_output (`torch.FloatTensor`): direct output from learned diffusion model.
    #         timestep (`int`): current discrete timestep in the diffusion chain.
    #         sample (`torch.FloatTensor`):
    #             current instance of sample being created by diffusion process.
    #         eta (`float`): weight of noise for added noise in diffusion step.
    #         use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped
    #             predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when
    #             `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would
    #             coincide with the one provided as input and `use_clipped_model_output` will have not effect.
    #         generator: random number generator.
    #         variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
    #             can directly provide the noise for the variance itself. This is useful for methods such as
    #             CycleDiffusion. (https://arxiv.org/abs/2210.05559)
    #         return_dict (`bool`): option for returning tuple rather than DDIMSchedulerOutput class

    #     Returns:
    #         [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
    #         [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
    #         returning a tuple, the first element is the sample tensor.

    #     """
    #     # print('DDIM step')
    #     if self.num_inference_steps is None:
    #         raise ValueError(
    #             "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
    #         )

    #     # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
    #     # Ideally, read DDIM paper in-detail understanding

    #     # Notation (<variable name> -> <name in paper>
    #     # - pred_noise_t -> e_theta(x_t, t)
    #     # - pred_original_sample -> f_theta(x_t, t) or x_0
    #     # - std_dev_t -> sigma_t
    #     # - eta -> η
    #     # - pred_sample_direction -> "direction pointing to x_t"
    #     # - pred_prev_sample -> "x_t-1"

    #     # 1. get previous step value (=t-1)
    #     prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps

    #     # 2. compute alphas, betas
    #     alpha_prod_t = self.alphas_cumprod[timestep]
    #     alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else torch.tensor(1.0)

    #     beta_prod_t = 1 - alpha_prod_t
    #     beta_prod_t_prev = 1 - alpha_prod_t_prev

    #     ### Correct coeff for DDIM: 
    #     epsilon_coeff = ((alpha_prod_t_prev ** (0.5)) * (beta_prod_t ** (0.5)) - (alpha_prod_t ** (0.5)) * (beta_prod_t_prev ** (0.5))) / (alpha_prod_t_prev ** (0.5))
        
    #     ### Correct coeff for DDIM step 1000: 
    #     ### epsilon_coeff = (1 - self.alphas[timestep]) / ((1 - alpha_prod_t) ** 0.5 + (self.alphas[timestep] - alpha_prod_t) ** 0.5)
    #     # trigger_coeff = (1 - (self.alphas[timestep] ** 0.5)) * (beta_prod_t ** 0.5) / (1 - self.alphas[timestep])
    #     prev_sample_tmp = sample - epsilon_coeff * model_output
        
    #     ### Correct for DDIM: 
    #     prev_sample = ((alpha_prod_t_prev ** (0.5)) / (alpha_prod_t ** (0.5))) * prev_sample_tmp
        
    #     ### Correct for DDIM step 1000: 
    #     ### prev_sample = (1 / (self.alphas[timestep] ** 0.5)) * prev_sample_tmp


    #     if not return_dict:
    #         return (prev_sample,)

    #     return DDPMSchedulerOutput(prev_sample=prev_sample, pred_original_sample=prev_sample_tmp)

    # def step(
    #     self,
    #     model_output: torch.FloatTensor,
    #     timestep: int,
    #     sample: torch.FloatTensor,
    #     predict_epsilon=True,
    #     generator=None,
    #     return_dict: bool = True,
    # ) -> Union[DDPMSchedulerOutput, Tuple]:
    #     """
    #     Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
    #     process from the learned model outputs (most often the predicted noise).

    #     Args:
    #         model_output (`torch.FloatTensor`): direct output from learned diffusion model.
    #         timestep (`int`): current discrete timestep in the diffusion chain.
    #         sample (`torch.FloatTensor`):
    #             current instance of sample being created by diffusion process.
    #         predict_epsilon (`bool`):
    #             optional flag to use when model predicts the samples directly instead of the noise, epsilon.
    #         generator: random number generator.
    #         return_dict (`bool`): option for returning tuple rather than DDPMSchedulerOutput class

    #     Returns:
    #         [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] or `tuple`:
    #         [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
    #         returning a tuple, the first element is the sample tensor.

    #     """
    #     t = timestep

    #     prev_t = self.previous_timestep(t) ### Added

    #     if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
    #         model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1)
    #     else:
    #         predicted_variance = None

    #     # 1. compute alphas, betas
    #     alpha_prod_t = self.alphas_cumprod[t]
    #     ### alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one
    #     alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one
    #     beta_prod_t = 1 - alpha_prod_t
    #     beta_prod_t_prev = 1 - alpha_prod_t_prev

    #     current_alpha_t = alpha_prod_t / alpha_prod_t_prev ### Added
    #     current_beta_t = 1 - current_alpha_t ### Added

    #     # 2. compute predicted original sample from predicted noise also called
    #     # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
    #     if predict_epsilon:
    #         pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
    #     else:
    #         pred_original_sample = model_output

    #     # 3. Clip "predicted x_0"
    #     if self.config.clip_sample:
    #         pred_original_sample = torch.clamp(pred_original_sample, -1, 1)

    #     # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
    #     # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
    #     ### pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * self.betas[t]) / beta_prod_t
    #     pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * current_beta_t) / beta_prod_t
    #     ### current_sample_coeff = self.alphas[t] ** (0.5) * beta_prod_t_prev / beta_prod_t
    #     current_sample_coeff = current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_t

    #     # 5. Compute predicted previous sample µ_t
    #     # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
    #     pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

    #     # 6. Add noise
    #     variance = 0
    #     # if t > 0:
    #     #     noise = torch.randn(
    #     #         model_output.size(), dtype=model_output.dtype, layout=model_output.layout, generator=generator
    #     #     ).to(model_output.device)
    #     #     variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * noise

    #     pred_prev_sample = pred_prev_sample + variance

    #     if not return_dict:
    #         return (pred_prev_sample,)

    #     return DDPMSchedulerOutput(prev_sample=pred_prev_sample, pred_original_sample=pred_original_sample)
    
    ### DDIM Step
    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        eta: float = 0.0,
        use_clipped_model_output: bool = False,
        generator=None,
        variance_noise: Optional[torch.FloatTensor] = None,
        return_dict: bool = True,
    ) -> Union[DDPMSchedulerOutput, Tuple]:
        """
        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
            timestep (`int`): current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                current instance of sample being created by diffusion process.
            eta (`float`): weight of noise for added noise in diffusion step.
            use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped
                predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when
                `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would
                coincide with the one provided as input and `use_clipped_model_output` will have not effect.
            generator: random number generator.
            variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
                can directly provide the noise for the variance itself. This is useful for methods such as
                CycleDiffusion. (https://arxiv.org/abs/2210.05559)
            return_dict (`bool`): option for returning tuple rather than DDIMSchedulerOutput class

        Returns:
            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
            returning a tuple, the first element is the sample tensor.

        """
        if self.num_inference_steps is None:
            raise ValueError(
                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
            )

        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
        # Ideally, read DDIM paper in-detail understanding

        # Notation (<variable name> -> <name in paper>
        # - pred_noise_t -> e_theta(x_t, t)
        # - pred_original_sample -> f_theta(x_t, t) or x_0
        # - std_dev_t -> sigma_t
        # - eta -> η
        # - pred_sample_direction -> "direction pointing to x_t"
        # - pred_prev_sample -> "x_t-1"

        # 1. get previous step value (=t-1)
        prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps

        # 2. compute alphas, betas
        alpha_prod_t = self.alphas_cumprod[timestep]
        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else torch.tensor(1.0)

        beta_prod_t = 1 - alpha_prod_t

        pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
        pred_epsilon = model_output
        # 3. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        # if self.config.prediction_type == "epsilon":
        #     pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
        #     pred_epsilon = model_output
        # elif self.config.prediction_type == "sample":
        #     pred_original_sample = model_output
        #     pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
        # elif self.config.prediction_type == "v_prediction":
        #     pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
        #     pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
        # else:
        #     raise ValueError(
        #         f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
        #         " `v_prediction`"
        #     )

        # # 4. Clip or threshold "predicted x_0"
        if self.config.clip_sample:
            pred_original_sample = pred_original_sample.clamp(
                -1, 1
            )

        # 5. compute variance: "sigma_t(η)" -> see formula (16)
        # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
        variance = self._get_variance(timestep, prev_timestep)
        std_dev_t = eta * variance ** (0.5)

        if use_clipped_model_output:
            # the pred_epsilon is always re-derived from the clipped x_0 in Glide
            pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)

        # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon

        # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction

        if eta > 0:
            if variance_noise is not None and generator is not None:
                raise ValueError(
                    "Cannot pass both generator and variance_noise. Please make sure that either `generator` or"
                    " `variance_noise` stays `None`."
                )

            if variance_noise is None:
                # variance_noise = randn_tensor(
                #     model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype
                # )
                variance_noise = torch.randn(model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype)
            variance = std_dev_t * variance_noise

            prev_sample = prev_sample + variance

        if not return_dict:
            return (prev_sample,)

        return DDPMSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
        timesteps: torch.IntTensor,
    ) -> torch.FloatTensor:
        # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
        self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
        timesteps = timesteps.to(original_samples.device)

        sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)

        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
        while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)

        noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
        return noisy_samples

    def __len__(self):
        return self.config.num_train_timesteps
    
    def previous_timestep(self, timestep):
        num_inference_steps = (
            self.num_inference_steps if self.num_inference_steps else self.config.num_train_timesteps
        )
        prev_t = timestep - self.config.num_train_timesteps // num_inference_steps

        return prev_t
